Integrate tan (x) with respect to x.

I = ∫ Tan (x) dx= ∫ (sin(x)) / (cos(x)) dx

We see that this is close to the standard integral ∫ F'(x) / F(x) dx = Ln (F(x)) + C

So first we must rewrite the Integral as: I = - ∫ (-sin(x)) / (cos(x)) dx (Taking minus one outside of the integral)

Now this is in the standard form and can be integrated;

I = - ∫ (-sin(x)) / (cos(x)) dx = - ln (cos (x)) + C